SCIENTIFIC NOTATION GUIDED NOTES AND PRACTICE

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SCIENTIFICNOTATION GUIDEDNOTES AND PRACTICEhcaTe yEas.XIncludes a 2 page notes/referencewith examples and practiceproblems, a 2 page student guidednotes with practice problems, anda worksheet with 24 practiceproblems!? Huh?

SCIENTIFIC NOTATIONRegular Notation (RN)- The standard way that we write our numbers.Ex: Two Hundred and Eight Million is written - 280,000,000.Scientific Notation (SN)- A shorthanded way of writing really large or really smallnumbers. In SN a number is written as the product of two factors.Ex: 280,000,000 can be written in scientific notation as 2.8 Β π‘₯ Β 10! .S eco nd F acto rIs always a power of 10.The power of the exponenttells you how many placesto move the decimal point.The sign of the exponenttells you which directionto move it.F irst Fa ctorA number that isbetween 1 and 10It may or may notbe a decimal.Regular Notation Γ  Scientific DecimalismovedtoRightExponentwillbenegativeHow to ChangeScientificNotationMove the decimal after the 4 and before the 2That is 5 places to the leftMultiply 4.2 by 10 to the 5th powerMove the decimal after the 7 and before the 3That is 8 places to the leftMultiply 7.35 by 10 to the 8th powerMove the decimal after the 8 and before the 9That is 3 places to the rightMultiply 8.97 by 10 to the -3rd powerMove the decimal after the 1 and before the 4That is 6 places to the rightMultiply 1.4 by 10 to the -6th power4.2 Β π‘₯ Β 10!7.35 Β π‘₯ Β 10!8.97 Β π‘₯ Β 10!!1.4 Β π‘₯ Β 10!!Copyright Shemiah Hale. All Rights Reserved

Scientific Notation Γ  Regular otheRightAddzeroswhereneeded.ScientificNotationHow to ChangeRegularNotation7.5 Β  Β 10!Exponent is positive 5.Move the decimal 5 places to the rightExponent is positive 4.Move the decimal 4 places to the rightExponent is Negative 3.Move the decimal 3 places to the left.Exponent is Negative 5.Move the decimal 5 places to the left.750,000.3.8 Β  Β 10!4.2 Β  Β 10!!7.51 Β  Β 10!!38,000.0042.0000751PRACTICE:Change from Regular Notation toScientific Notation:Change from Scientific Notation toRegular Notation:1.) Β 45,0002.) Β 9,000,0003.) Β 7,4504.) Β .00003785.) Β .056.) Β 670,4007.) Β 7,070,000,0008.) Β .000000899.) Β .1890009710.) Β 570,000,0001.) Β 9.46 Β  Β 10!!2.) Β 2.5 Β  Β 10!3.) Β 1.6 Β  Β 10!!4.) Β 4 Β  Β 10 Β !5.) Β 7.25 Β  Β 10 Β !6.) Β 3.2456 Β  Β 10!!7.) Β 6 Β  Β 10!!8.) Β 9.7 Β  Β 10!9.) Β 5.06 Β  Β 10!!10.) Β 8 Β  Β 10!Copyright Shemiah Hale. All Rights Reserved

SCIENTIFIC NOTATIONRegular Notation (RN)- The that we write our numbers.Ex: Two Hundred and Eight Million is written -Scientific Notation (SN)- A of writing really large or reallysmall numbers. In SN a number is written as the of .Ex: 280,000,000 can be written in scientific notation asS eco nd F acto rIs always aThe power of the exponenttells youto move the decimal point.The of theexponent tells you whichto move it.F irst Fa ctorA number that is.It may or may notbe .Regular Notation Γ  Scientific ovedto.Exponentwillbe.How to ChangeScientificNotationMove the decimal after the 4 and before the 2That is 5 places to the leftMultiply 4.2 by 10 to the 5th powerMove the decimal after the 7 and before the 3That is 8 places to the leftMultiply 7.35 by 10 to the 8th powerMove the decimal after the 8 and before the 9That is 3 places to the rightMultiply 8.97 by 10 to the -3rd powerMove the decimal after the 1 and before the 4That is 6 places to the rightMultiply 1.4 by 10 to the -6th powerCopyright Shemiah Hale. All Rights Reserved

Scientific Notation Γ  Regular ded.ScientificNotationHow to Change7.5 Β  Β 10!Exponent is positive 5.Move the decimal 5 places to the rightExponent is positive 4.Move the decimal 4 places to the rightExponent is Negative 3.Move the decimal 3 places to the left.Exponent is Negative 5.Move the decimal 5 places to the left.3.8 Β  Β 10!4.2 Β  Β 10!!7.51 Β  Β 10!!RegularNotationPRACTICE:Change from Regular Notation toScientific Notation:Change from Scientific Notation toRegular Notation:1.) Β 45,0002.) Β 9,000,0003.) Β 7,4504.) Β .00003785.) Β .056.) Β 670,4007.) Β 7,070,000,0008.) Β .000000899.) Β .1890009710.) Β 570,000,0001.) Β 9.46 Β  Β 10!!2.) Β 2.5 Β  Β 10!3.) Β 1.6 Β  Β 10!!4.) Β 4 Β  Β 10 Β !5.) Β 7.25 Β  Β 10 Β !6.) Β 3.2456 Β  Β 10!!7.) Β 6 Β  Β 10!!8.) Β 9.7 Β  Β 10!9.) Β 5.06 Β  Β 10!!10.) Β 8 Β  Β 10!Copyright Shemiah Hale. All Rights Reserved

ANSWER KEY:Change from Regular Notation toScientific Notation:1.) Β 45,0002.) Β 9,000,0003.) Β 7,4504.) Β .00003785.) Β .056.) Β 670,4007.) Β 7,070,000,0008.) Β .000000899.) Β .1890009710.) Β 570,000,0004.5 Β π‘₯ Β 10!9 Β π‘₯ Β 10!7.45 Β π‘₯ Β 10!3.78 Β π‘₯ Β 10!!5 Β π‘₯ Β 10!!6.704 Β π‘₯ Β 10!7.070 Β π‘₯ Β 10!8.9 Β π‘₯ Β 10!!1.8900097 Β π‘₯ Β 10!!5.7 Β π‘₯ Β 10!Change from Scientific Notation toRegular Notation:1.) Β 9.46 Β  Β 10!!2.) Β 2.5 Β  Β 10!3.) Β 1.6 Β  Β 10!!4.) Β 4 Β  Β 10 Β !5.) Β 7.25 Β  Β 10 Β !6.) Β 3.2456 Β  Β 10!!7.) Β 6 Β  Β 10!!8.) Β 9.7 Β  Β 10!9.) Β 5.06 Β  Β 10!!10.) Β 8 Β  0697,000,000.000506800Copyright Shemiah Hale. All Rights Reserved

STUDENT NAME: DATE:SCIENTIFIC NOTATIONCONVERT EACH NUMBER INSCIENTIFIC NOTATION TO REGULAR otheRightAddzeroswhereneeded.1. 𝟐. πŸ’πŸ•  𝒙  𝟏𝟎!πŸ‘7. πŸ’. πŸ“  𝒙  𝟏𝟎!πŸ“2. πŸ—. πŸ‘  𝒙 Β πŸπŸŽπŸ•8.πŸ“. πŸ“  𝒙  𝟏𝟎 Β πŸ“3. πŸ–. πŸ“  𝒙  𝟏𝟎!πŸ“9. πŸ”. πŸ‘  𝒙  𝟏𝟎!𝟏4. 𝟐. πŸŽπŸ•  𝒙  𝟏𝟎 Β πŸ”10. 𝟏. πŸ—πŸ–  𝒙  𝟏𝟎 Β πŸ’5. πŸ•  𝒙  𝟏𝟎!πŸ–11.  𝟐. πŸ’  𝒙  𝟏𝟎!πŸ“6. πŸ‘  𝒙  𝟏𝟎  𝟐12. πŸ—. 𝟐  𝒙  𝟏𝟎 Β πŸ•CONVERT EACH NUMBER INREGULAR NOTATION TO SCIENTIFIC IfDecimalismovedtoRightExponentwillbenegative1. 0.00247. 0.00000352. 5,6048. 45,9953. 693.759. 754.2564. 0.08710. 0.00885. 8,550,00011. 1.89076. 12,000,00012. 25,009

Answer keySCIENTIFIC NOTATIONCONVERT EACH NUMBER INSCIENTIFIC NOTATION TO REGULAR otheRightAddzeroswhereneeded.1. 𝟐. πŸ’πŸ•  𝒙  𝟏𝟎!πŸ‘0.02477. πŸ’. πŸ“  𝒙  𝟏𝟎!πŸ“0.0000452. πŸ—. πŸ‘  𝒙 Β πŸπŸŽπŸ•93,000,0008. Β  Β πŸ“. πŸ“  𝒙  𝟏𝟎 Β πŸ“550,0003. πŸ–. πŸ“  𝒙  𝟏𝟎!πŸ“0.0000859. πŸ”. πŸ‘  𝒙  𝟏𝟎!𝟏0.634. 𝟐. πŸŽπŸ•  𝒙  𝟏𝟎 Β πŸ”2,070,00010. 𝟏. πŸ—πŸ–  𝒙  𝟏𝟎 Β πŸ’19,8005. πŸ•  𝒙  𝟏𝟎!πŸ–0.0000000711.  𝟐. πŸ’  𝒙  𝟏𝟎!πŸ“0.0000246. πŸ‘  𝒙  𝟏𝟎  𝟐30012. πŸ—. 𝟐  𝒙  𝟏𝟎 Β πŸ•92,000,000CONVERT EACH NUMBER INREGULAR NOTATION TO SCIENTIFIC IfDecimalismovedtoRightExponentwillbenegative1. 0.0024𝟐. πŸ’  𝒙  𝟏𝟎!πŸ‘7. 0.0000035πŸ‘. πŸ“  𝒙  𝟏𝟎!πŸ”2. 5,604πŸ“. πŸ”πŸŽπŸ’  𝒙  𝟏𝟎 Β πŸ‘8. 45,995πŸ’. πŸ“πŸ—πŸ—πŸ“  𝒙  𝟏𝟎 Β πŸ’3. 693.75πŸ”. πŸ—πŸ‘πŸ•πŸ“  𝒙  𝟏𝟎  𝟐9. 754.256πŸ•. πŸ“πŸ’πŸπŸ“πŸ”  𝒙  𝟏𝟎𝟐4. 0.087πŸ–. πŸ•  𝒙  𝟏𝟎  𝟐10. 0.0088πŸ–. πŸ–  𝒙  𝟏𝟎!πŸ‘5. 8,550,000πŸ–. πŸ“πŸ“πŸŽ  𝒙  𝟏𝟎!πŸ”11. 18.907𝟏. πŸ–  𝒙  𝟏𝟎  𝟏6. 12,000,000𝟏. 𝟐  𝒙  𝟏𝟎 Β πŸ•12. 25,009𝟐. πŸ“πŸŽπŸŽπŸ—  𝒙  𝟏𝟎 Β πŸ’

Scientific Notation (SN)- A shorthanded way of writing really large or really small numbers. In SN a number is written as the product of two factors. !Ex: 280,000,000 can be written in scientific notation as 2.8!!!10. First Factor Regular Notation ! Scientific Notation Regular Notation How to Change Scientific Notation 420,000.

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